Question

a corporation must appoint a president, chief executive officer (ceo), chief operating officer (coo), and chief financial officer (cfo). it must also appoint a planning committee with four different members. there are 15 qualified candidates, and officers can also serve on the committee. complete parts (a) through (c) below.
a. how many different ways can the four officers be appointed?
there are 32760 different ways to appoint the four officers.
b. how many different ways can a committee of four be appointed?
there are 1365 different ways to appoint a committee of four.
c. what is the probability of randomly selecting the committee members and getting the four youngest of the qualified candidates?
p(getting the four youngest of the qualified candidates) = (type an integer or a simplified fraction.)

Explanation:

Step1: Recall probability formula

The probability $P(E)$ of an event $E$ is given by $P(E)=\frac{n(E)}{n(S)}$, where $n(E)$ is the number of favorable outcomes and $n(S)$ is the total number of outcomes.

Step2: Identify favorable and total outcomes

The number of favorable outcomes $n(E)$ of getting the four - youngest candidates is 1 (since there is only one set of the four - youngest candidates). The total number of ways to appoint a committee of four from 15 candidates $n(S)$ is 1365 (from part b).

Step3: Calculate probability

$P=\frac{n(E)}{n(S)}=\frac{1}{1365}$

Answer:

$\frac{1}{1365}$